Biomedical subjects
Publications and source records attributed to Lars Kai Hansen.
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We use a Bayesian framework to detect periodic components in fMRI data. The resulting detector is sensitive to periodic components with a flexible number of harmonics and with arbitrary amplitude and phases of the harmonics. It is possible to detect the correct number of harmonics in periodic signals even if the fundamental frequency is beyond the Nyquist frequency. We apply the signal detector to locate regions that are highly affected by periodic physiological artifacts, such as cardiac pulsation.
We develop mean-field approaches for probabilistic independent component analysis (ICA). The sources are estimated from the mean of their posterior distribution and the mixing matrix (and noise level) is estimated by maximum a posteriori (MAP). The latter requires the computation of (a good approximation to) the correlations between sources. For this purpose, we investigate three increasingly advanced mean-field methods: the variational (also known as naive mean field) approach, linear response corrections, and an adaptive version of the Thouless, Anderson and Palmer (1977) (TAP) mean-field approach, which is due to Opper and Winther (2001). The resulting algorithms are tested on a number of problems. On synthetic data, the advanced mean-field approaches are able to recover the correct mixing matrix in cases where the variational meanfield theory fails. For handwritten digits, sparse encoding is achieved using nonnegative source and mixing priors. For speech, the mean-field method is able to separate in the underdetermined (overcomplete) case of two sensors and three sources. One major advantage of the proposed method is its generality and algorithmic simplicity. Finally, we point out several possible extensions of the approaches developed here.
In this paper we propose a method for construction of feed-forward neural classifiers based on regularization and adaptive architectures. Using a penalized maximum likelihood scheme, we derive a modified form of the entropic error measure and an algebraic estimate of the test error. In conjunction with optimal brain damage pruning, a test error estimate is used to select the network architecture. The scheme is evaluated on four classification problems.
We investigate the use of a regularization prior and its pruning properties. We illustrate the behavior of this prior by conducting analyses both using a Bayesian framework and with the generalization method, on a simple toy problem. Results are thoroughly compared with those obtained with a traditional weight decay. Copyright 1997 Elsevier Science Ltd.